From: mikegold@umich.edu (Michael Paul Goldenberg)
Newsgroups: k12.ed.math
Subject: Re: created or discovered?
Date: Sat, 30 Aug 1997 17:29:11 GMT
Organization: University of Michigan
Lines: 69
Sender: k12math@sd28.bc.ca
Approved: k12math@sd28.bc.ca

I basically agree with most of what Darrell has written. Two points need
making, however. First, 'gravity' didn't exist, if Darrell's overall
thinking about mathematics is correct, until someone gave it a name.
However, the phenomena associated with what we have chosen to give the
name 'gravity' as a kind of mental shorthand (e.g., "Gee, here are some
interesting things that seem to be related: let's call them 'gravity.'")
have pretty much always existed. So the issue here isn't whether 'reality'
exists, in case any platonists are getting nervous, but rather that the
concepts into which we choose to divide up reality are invented. Do we
have totally free reign as to how to see things? Probably not. There are
limits which involve the interplay of 'what's really out there' and 'the
way our brains work.' Indeed, it may be that there are some definite
relationships of significance between those two realms. But we need to be
reminded rather frequently that virtually everything we categorize as "X"
could just have easily be lumped into some other category, depending upon
whim and the categorization scheme we're employing.

WHich leads me to Darrell's comment on dogs and cats. The important point
to remember is not the what we call a dog could just as easily have be
called a host of other things, including 'cat', but that what we call dogs
could have remained lumped into some larger category (e.g., canines, or a
category that only included coyotes and dogs) or a smaller one (imagine,
for example, a language which had words for canines, wolves, coyotes,
etc., and for every imaginable breed of dog, but which lacked a generic
word for 'dog').

So language, while not creating reality, perhaps, certainly reflects
certain human categories, arbitrary and non-natural, with which a group of
people, over time, have chosen to cut up their reality. But no such scheme
can cut reality 'at its joints' because no such joints exist. Reality is
seamless. We make the seams to suit our purposes, but should try to recall
that we did so.

Sorry to go all linguistic on you. But you know how we former English
teachers can get. ;^)

-- 
"Truth is a mobile army of metaphors." - F. Nietzsche


----------------------------
message approved for posting by k12.ed.math moderator:Sheila King
k12.ed.math is a moderated newsgroup.
charter for the newsgroup at www.wenet.net/~cking/sheila/charter.html
submissions: post to k12.ed.math or e-mail to k12math@sd28.bc.ca